Cyclic Cohomology of the Weyl Algebra

循环同调、$S^1$-等变Floer上同调与Calabi-Yau结构

Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures

本文构造Fukaya范畴循环同调到$S^1$-等变上同调的循环开-闭映射，用以建立Calabi-Yau结构并证明非交换Hodge-de Rham退化。

Notes on Kontsevich-Soibelman's theorem about cyclic A-infinity algebras

Kontsevich and Soibelman has proved a relation between a non-degenerate cyclic homology element of an A-infinity algebra A and its cyclic inner products on the minimal model of A. We find an explicit formula of this correspondence, in terms of the strong homotopy inner products and negative cyclic cohomology of A. We prove that an equivalence class of the induced strong homotopy inner product depends only on the given negative cyclic cohomology class. Also, we extend such a correspondence to the case of gapped filtered A-infinity algebras.

Cyclic Homology of Fukaya Categories and the Linearized Contact Homology

Let $M$ be an exact symplectic manifold with contact type boundary such that $c_1(M)=0$. In this paper we show that the cyclic cohomology of the Fukaya category of $M$ has the structure of an involutive Lie bialgebra. Inspired by a work of Cieliebak-Latschev we show that there is a Lie bialgebra homomorphism from the linearized contact homology of $M$ to the cyclic cohomology of the Fukaya category. Our study is also motivated by string topology and 2-dimensional topological conformal field theory.